Where to Buy Arcade Controls and Parts

Arcade Controls

Happ Controls
The main distributor of arcade controls. I believe they may have required minimums on orders. (Could someone confirm this?)

Centsible Amusements
Has the same parts as Happs and located in Florida so if your on the east coast they're very fast and often a bit cheaper. They also have a few more payment options which may open the doors from some people. Highly recommended!

Check your local arcades to see if they have extra parts. Even if they charge you for soem buttons it beats waiting on shipping.

Ebay is an option as well. You may not be able to find parts alone but keep an eye out for any 'arcade sticks'. Even if you find a stick for another system you could easily salvage parts (just make sure it's got the parts you want, ask the seller if the description doesn't say). Arcade controls are designed to take a beating so they should be usable. Avoid buying used joysticks that have leaf switches (as opposed to microswitches), since those Can wear out over time.

Hardware

Obviously you'll want to pay a nearby hardware store a visit for box building materials. Home Depot, Builders Square etc. Most of these places can make any simple cuts for you so take advantage of this. Typically this service is free for five or so cuts.
You'll also want to get your hinges here as they'll have a good selection to pick from. If your planning on getting a table saw you should be able to find a small one for around $100 (you shouldn't need anything massive for this project alone).
Avoid Sears unless you dislike money. I'm not dogging on Sears in general but for the needs of this project they have nothing to offer that you can't get elsewhere cheaper.

Electronics

If your local gaming store doesn't have the pad your looking for, ebay is a goldmine for gamepads. Remember that you only need the circuit board so that "broken gamepad 99cents" may be exactly what your looking for. It's very rare for the board in a gamepad to be broken, usually it's the case that's bad. Just make sure the guy's dog didn't chew up the cord.
Radio Shack has wire, solder, desoldering braid and just about any other electrical thing you could possibly want.